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 Mat. Sb., 1991, Volume 182, Number 3, Pages 431–456 (Mi msb1304)

Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix

V. A. Yurko

Saratov State University named after N. G. Chernyshevsky

Abstract: The inverse problem of recovering differential operators
$$ly=y^{(n)}+\sum_{\nu=0}^{n-2}p_\nu(x)y^{(\nu)}, \qquad x>0,$$
from the Weyl matrix is investigated. A solution of this problem is given for arbitrary behavior of the spectrum, along with necessary and sufficient conditions and a uniqueness theorem.

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English version:
Mathematics of the USSR-Sbornik, 1992, 72:2, 413–438

Bibliographic databases:

UDC: 517.9
MSC: 34A55, 34L05

Citation: V. A. Yurko, “Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix”, Mat. Sb., 182:3 (1991), 431–456; Math. USSR-Sb., 72:2 (1992), 413–438

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yurko V., “The Inverse Problem for Self-Adjoint Differential-Operators on the Half-Line”, Dokl. Akad. Nauk, 333:4 (1993), 449–451
2. Yurko V., “On Higher-Order Differential-Operators with a Singular Point”, Inverse Probl., 9:4 (1993), 495–502
3. V. A. Yurko, “On higher-order differential operators with a regular singularity”, Sb. Math., 186:6 (1995), 901–928
4. V. A. Yurko, “On determination of self-adjoint differential operators on a semiaxis”, Math. Notes, 57:3 (1995), 310–318
5. V. A. Yurko, “Integrations of nonlinear dynamic systems with the method of inverse spectral problems”, Math. Notes, 57:6 (1995), 672–675
6. V. A. Yurko, “On discrete operators of higher order”, Russian Math. Surveys, 51:3 (1996), 578–580
7. Yurko V., “On Boundary Value Problems for Differential Equations with a Singular Point”, Dokl. Akad. Nauk, 349:4 (1996), 460–462
8. Yurko V., “Inverse Problem for Systems of Differential Equations with Nonlinear Dependence on a Spectral Parameter”, Differ. Equ., 33:3 (1997), 388–394
9. V. A. Yurko, “Integrable dynamical systems associated with higher-order difference operators”, Russian Math. (Iz. VUZ), 42:10 (1998), 69–79
10. M. M. Malamud, “Borg Type Theorems for First-Order Systems on a Finite Interval”, Funct. Anal. Appl., 33:1 (1999), 64–68
11. Freiling G. Yurko V., “Inverse Spectral Problems for Differential Equations on the Half-Line with Turning Points”, J. Differ. Equ., 154:2 (1999), 419–453
12. Fritz Gesztesy, Eduard Tsekanovskii, “On Matrix-Valued Herglotz Functions”, Math Nachr, 218:1 (2000), 61
13. V. A. Yurko, “An inverse problem for differential operator pencils”, Sb. Math., 191:10 (2000), 1561–1586
14. V. A. Yurko, “Reconstruction of pencils of differential operators on the half-line”, Math. Notes, 67:2 (2000), 261–265
15. Kravchenko K., “Differential Operators with Nonlocal Boundary Conditions”, Differ. Equ., 36:4 (2000), 517–523
16. Yurko V., “An Inverse Problem for Differential Operators of the Orr-Sommerfeld Type”, Math. Nachr., 211 (2000), 177–183
17. V. Yurko, “Recovery of differential equations with nonlinear dependence on the spectral parameter”, Applicable Analysis, 78:1-2 (2001), 63
18. Mennicken R., Sakhnovich A., Tretter C., “Direct and Inverse Spectral Problem for a System of Differential Equations Depending Rationally on the Spectral Parameter”, Duke Math. J., 109:3 (2001), 413–449
19. V. A. Yurko, “Reconstruction of Non-Self-Adjoint Differential Systems on the Half-Line from the Weyl Matrix”, Math. Notes, 76:2 (2004), 296–302
20. V. A. Yurko, “An inverse spectral problem for singular non-self-adjoint differential systems”, Sb. Math., 195:12 (2004), 1823–1854
21. Yurko V., “Necessary and Sufficient Conditions for the Solvability of an Inverse Problem for Systems of Differential Equations on a Half-Line”, Dokl. Math., 69:3 (2004), 465–468
22. V. Yurko, “An inverse spectral problem for differential systems on the half-line with multiplied roots of the characteristic polynomial”, j inv ill-posed problems, 13:5 (2005), 503
23. Yurko, VA, “An inverse problem for differential systems on a finite interval in the case of multiple roots of the characteristic polynomial”, Differential Equations, 41:6 (2005), 818
24. Malamud M.M., “Borg-Type Theorems for High-Order Equations with Matrix Coefficients”, Dokl. Math., 74:1 (2006), 528–532
25. Wuqing Ning, “An inverse spectral problem for a nonsymmetric differential operator: Reconstruction of eigenvalue problem”, Journal of Mathematical Analysis and Applications, 327:2 (2007), 1396
26. Ning, W, “On stability of an inverse spectral problem for a nonsymmetric differential operator”, Journal of Inverse and Ill-Posed Problems, 17:3 (2009), 289
27. Alexander Sakhnovich, “Construction of the Solution of the Inverse Spectral Problem for a System Depending Rationally on the Spectral Parameter, Borg–Marchenko-Type Theorem and sine-Gordon Equation”, Integr. Equ. Oper. Theory, 2010
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